Average Error: 35.1 → 30.9
Time: 35.4s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;g \le -5.110014296461794 \cdot 10^{-199}:\\ \;\;\;\;\frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\sqrt[3]{2 \cdot a}} + \frac{\sqrt[3]{\sqrt[3]{\sqrt{g \cdot g - h \cdot h}} \cdot \left(\sqrt[3]{\sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h}}\right) + \left(-g\right)}}{\sqrt[3]{2 \cdot a}}\\ \mathbf{elif}\;g \le 6.420654691865451 \cdot 10^{-40}:\\ \;\;\;\;\sqrt[3]{\left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right) \cdot \frac{1}{2 \cdot a}} + \frac{\sqrt[3]{\left(-g\right) - g}}{\sqrt[3]{2 \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{g \cdot g - \sqrt{g \cdot g - h \cdot h} \cdot \sqrt{g \cdot g - h \cdot h}}}{\sqrt[3]{\left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right) \cdot \left(2 \cdot a\right)}} + \frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\sqrt[3]{2 \cdot a}}\\ \end{array}\]
\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}
↓
\begin{array}{l}
\mathbf{if}\;g \le -5.110014296461794 \cdot 10^{-199}:\\
\;\;\;\;\frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\sqrt[3]{2 \cdot a}} + \frac{\sqrt[3]{\sqrt[3]{\sqrt{g \cdot g - h \cdot h}} \cdot \left(\sqrt[3]{\sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h}}\right) + \left(-g\right)}}{\sqrt[3]{2 \cdot a}}\\

\mathbf{elif}\;g \le 6.420654691865451 \cdot 10^{-40}:\\
\;\;\;\;\sqrt[3]{\left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right) \cdot \frac{1}{2 \cdot a}} + \frac{\sqrt[3]{\left(-g\right) - g}}{\sqrt[3]{2 \cdot a}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\sqrt[3]{g \cdot g - \sqrt{g \cdot g - h \cdot h} \cdot \sqrt{g \cdot g - h \cdot h}}}{\sqrt[3]{\left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right) \cdot \left(2 \cdot a\right)}} + \frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\sqrt[3]{2 \cdot a}}\\

\end{array}
double f(double g, double h, double a) {
        double r5121979 = 1.0;
        double r5121980 = 2.0;
        double r5121981 = a;
        double r5121982 = r5121980 * r5121981;
        double r5121983 = r5121979 / r5121982;
        double r5121984 = g;
        double r5121985 = -r5121984;
        double r5121986 = r5121984 * r5121984;
        double r5121987 = h;
        double r5121988 = r5121987 * r5121987;
        double r5121989 = r5121986 - r5121988;
        double r5121990 = sqrt(r5121989);
        double r5121991 = r5121985 + r5121990;
        double r5121992 = r5121983 * r5121991;
        double r5121993 = cbrt(r5121992);
        double r5121994 = r5121985 - r5121990;
        double r5121995 = r5121983 * r5121994;
        double r5121996 = cbrt(r5121995);
        double r5121997 = r5121993 + r5121996;
        return r5121997;
}
↓
double f(double g, double h, double a) {
        double r5121998 = g;
        double r5121999 = -5.110014296461794e-199;
        bool r5122000 = r5121998 <= r5121999;
        double r5122001 = -r5121998;
        double r5122002 = r5121998 * r5121998;
        double r5122003 = h;
        double r5122004 = r5122003 * r5122003;
        double r5122005 = r5122002 - r5122004;
        double r5122006 = sqrt(r5122005);
        double r5122007 = r5122001 - r5122006;
        double r5122008 = cbrt(r5122007);
        double r5122009 = 2.0;
        double r5122010 = a;
        double r5122011 = r5122009 * r5122010;
        double r5122012 = cbrt(r5122011);
        double r5122013 = r5122008 / r5122012;
        double r5122014 = cbrt(r5122006);
        double r5122015 = r5122014 * r5122014;
        double r5122016 = r5122014 * r5122015;
        double r5122017 = r5122016 + r5122001;
        double r5122018 = cbrt(r5122017);
        double r5122019 = r5122018 / r5122012;
        double r5122020 = r5122013 + r5122019;
        double r5122021 = 6.420654691865451e-40;
        bool r5122022 = r5121998 <= r5122021;
        double r5122023 = r5122001 + r5122006;
        double r5122024 = 1.0;
        double r5122025 = r5122024 / r5122011;
        double r5122026 = r5122023 * r5122025;
        double r5122027 = cbrt(r5122026);
        double r5122028 = r5122001 - r5121998;
        double r5122029 = cbrt(r5122028);
        double r5122030 = r5122029 / r5122012;
        double r5122031 = r5122027 + r5122030;
        double r5122032 = r5122006 * r5122006;
        double r5122033 = r5122002 - r5122032;
        double r5122034 = cbrt(r5122033);
        double r5122035 = r5122007 * r5122011;
        double r5122036 = cbrt(r5122035);
        double r5122037 = r5122034 / r5122036;
        double r5122038 = r5122037 + r5122013;
        double r5122039 = r5122022 ? r5122031 : r5122038;
        double r5122040 = r5122000 ? r5122020 : r5122039;
        return r5122040;
}

Error

Bits error versus g

Bits error versus h

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if g < -5.110014296461794e-199

    1. Initial program 33.9

      \[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
    2. Using strategy rm

    3. Applied associate-*l/33.9

      \[\leadsto \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\color{blue}{\frac{1 \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}{2 \cdot a}}}\]

    4. Applied cbrt-div33.8

      \[\leadsto \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \color{blue}{\frac{\sqrt[3]{1 \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}}{\sqrt[3]{2 \cdot a}}}\]
    5. Using strategy rm

    6. Applied associate-*l/33.8

      \[\leadsto \sqrt[3]{\color{blue}{\frac{1 \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)}{2 \cdot a}}} + \frac{\sqrt[3]{1 \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}}{\sqrt[3]{2 \cdot a}}\]

    7. Applied cbrt-div30.6

      \[\leadsto \color{blue}{\frac{\sqrt[3]{1 \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)}}{\sqrt[3]{2 \cdot a}}} + \frac{\sqrt[3]{1 \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}}{\sqrt[3]{2 \cdot a}}\]
    8. Using strategy rm

    9. Applied add-cube-cbrt30.6

      \[\leadsto \frac{\sqrt[3]{1 \cdot \left(\left(-g\right) + \color{blue}{\left(\sqrt[3]{\sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h}}\right) \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h}}}\right)}}{\sqrt[3]{2 \cdot a}} + \frac{\sqrt[3]{1 \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}}{\sqrt[3]{2 \cdot a}}\]

    if -5.110014296461794e-199 < g < 6.420654691865451e-40

    1. Initial program 28.8

      \[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
    2. Using strategy rm

    3. Applied associate-*l/28.8

      \[\leadsto \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\color{blue}{\frac{1 \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}{2 \cdot a}}}\]

    4. Applied cbrt-div23.1

      \[\leadsto \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \color{blue}{\frac{\sqrt[3]{1 \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}}{\sqrt[3]{2 \cdot a}}}\]

    5. Taylor expanded around inf 18.0

      \[\leadsto \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \frac{\sqrt[3]{1 \cdot \left(\left(-g\right) - \color{blue}{g}\right)}}{\sqrt[3]{2 \cdot a}}\]

    if 6.420654691865451e-40 < g

    1. Initial program 38.2

      \[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
    2. Using strategy rm

    3. Applied associate-*l/38.2

      \[\leadsto \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\color{blue}{\frac{1 \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}{2 \cdot a}}}\]

    4. Applied cbrt-div34.9

      \[\leadsto \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \color{blue}{\frac{\sqrt[3]{1 \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}}{\sqrt[3]{2 \cdot a}}}\]
    5. Using strategy rm

    6. Applied flip-+34.9

      \[\leadsto \sqrt[3]{\frac{1}{2 \cdot a} \cdot \color{blue}{\frac{\left(-g\right) \cdot \left(-g\right) - \sqrt{g \cdot g - h \cdot h} \cdot \sqrt{g \cdot g - h \cdot h}}{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}} + \frac{\sqrt[3]{1 \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}}{\sqrt[3]{2 \cdot a}}\]

    7. Applied frac-times34.9

      \[\leadsto \sqrt[3]{\color{blue}{\frac{1 \cdot \left(\left(-g\right) \cdot \left(-g\right) - \sqrt{g \cdot g - h \cdot h} \cdot \sqrt{g \cdot g - h \cdot h}\right)}{\left(2 \cdot a\right) \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}}} + \frac{\sqrt[3]{1 \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}}{\sqrt[3]{2 \cdot a}}\]

    8. Applied cbrt-div34.8

      \[\leadsto \color{blue}{\frac{\sqrt[3]{1 \cdot \left(\left(-g\right) \cdot \left(-g\right) - \sqrt{g \cdot g - h \cdot h} \cdot \sqrt{g \cdot g - h \cdot h}\right)}}{\sqrt[3]{\left(2 \cdot a\right) \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}}} + \frac{\sqrt[3]{1 \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}}{\sqrt[3]{2 \cdot a}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification30.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;g \le -5.110014296461794 \cdot 10^{-199}:\\ \;\;\;\;\frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\sqrt[3]{2 \cdot a}} + \frac{\sqrt[3]{\sqrt[3]{\sqrt{g \cdot g - h \cdot h}} \cdot \left(\sqrt[3]{\sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h}}\right) + \left(-g\right)}}{\sqrt[3]{2 \cdot a}}\\ \mathbf{elif}\;g \le 6.420654691865451 \cdot 10^{-40}:\\ \;\;\;\;\sqrt[3]{\left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right) \cdot \frac{1}{2 \cdot a}} + \frac{\sqrt[3]{\left(-g\right) - g}}{\sqrt[3]{2 \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{g \cdot g - \sqrt{g \cdot g - h \cdot h} \cdot \sqrt{g \cdot g - h \cdot h}}}{\sqrt[3]{\left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right) \cdot \left(2 \cdot a\right)}} + \frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\sqrt[3]{2 \cdot a}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019138 
(FPCore (g h a)
  :name "2-ancestry mixing, positive discriminant"
  (+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))))